By applying the inner product of vectors, two objective functions are found. These vectors are taken from the structural equilibrium path. Via minimizing these functions, with respect to the load incremental parameter and the angle between particular vectors, two new constraint equalities are achieved. Since the scheme of authors is general, three more constraints are also reached. These formulations are similar to the previous presented nonlinear solvers, which confirm the legitimacy of new procedure. Afterward, several numerical tests are performed to prove the ability of the proposed techniques. Findings show that the new algorithms are capable in passing the load and displacement limit points of the various benchmark problems with severe nonlinear behaviors. Based on the number of increments and iterations and also the total analysis duration, the suggested methods have the maximum rapid convergence rate, in comparison to the normal plane, the updated normal plane and the cylindrical arc length strategies.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.